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A133319
Dimensions of certain Lie algebra (see reference for precise definition).
1
1, 99, 3927, 89661, 1387386, 15991118, 146005860, 1102439052, 7104607224, 40026446824, 200870048808, 911470725816, 3785393728644, 14533745396940, 52021580746190, 174825979846650, 554970843001575, 1672767047791125, 4809070448807625, 13239084661963875
OFFSET
0,2
LINKS
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), pp. 143-179. [Th. 7.2(i), case a = 6]
MAPLE
b:=binomial; t72a:= proc(a, k) ((2*a+2*k+1)/(2*a+1)) * b(k+3*a/2-1, k)*b(k+3*a/2+1, k)*b(k+2*a, k)/(b(k+a/2-1, k)*b(k+a/2+1, k)); end; [seq(t72a(6, k), k=0..40)];
MATHEMATICA
t72a[a_, k_] := (2k+2a+1) / (2a+1) Binomial[k+3/2a-1, k] Binomial[k+3/2a+1, k] Binomial[k+2a, k] / (Binomial[k+a/2-1, k] Binomial[k+a/2+1, k]);
Array[t72a[6, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)
CROSSREFS
Sequence in context: A246247 A157370 A163040 * A196745 A196903 A017815
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2007
STATUS
approved